Sample QuestionsExponents Of Real Numbers [NEW] questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Which of the following is not equal to $\left\{\left(\frac{5}{6}\right)^{1 / 5}\right\}^{-1 / 6} ?$
- ✓
$\left(\frac{5}{6}\right)^{\frac{1}{5}-\frac{1}{6}}$
- B
$1 \div\left\{\left(\frac{5}{6}\right)^{1 / 5}\right\}^{1 / 6}$
- C
$\left(\frac{6}{5}\right)^{\frac{1}{30}}$
- D
$\left(\frac{5}{6}\right)^{-\frac{1}{30}}$
Answer: A.
View full solution →Which of the following is equal to x?
- A
$x^{\frac{12}{7}}-x^{-\frac{5}{7}}$
- B
$\sqrt[12]{\left(x^4\right)^{1 / 3}}$
- ✓
$\left(\sqrt{x^3}\right)^{2 / 3}$
- D
$x^{\frac{12}{7}} \times x^{\frac{7}{12}}$
Answer: C.
View full solution →Value of $\sqrt[4]{(81)^{-2}}$ is
- ✓
$\frac{1}{9}$
- B
$\frac{1}{3}$
- C
- D
$\frac{1}{81}$
Answer: A.
View full solution →The product $\sqrt[3]{2} \times \sqrt[4]{2} \times \sqrt[12]{32}$ equals
- A
$\sqrt{2}$
- ✓
- C
$\sqrt[12]{2}$
- D
$\sqrt[12]{32}$
Answer: B.
View full solution →$\sqrt[4]{\sqrt[3]{2^2}}$ equals
- A
$2^{-1 / 6}$
- B
$2^{-6}$
- ✓
$2^{1 / 6}$
- D
$2^6$
Answer: C.
View full solution →Statement-1 (A): $\sqrt{\frac{81}{64} \sqrt{\frac{81}{64} \sqrt{\frac{81}{64} \sqrt{\frac{81}{64}}}}} \cdots \cdot x=\frac{9}{8}$,
Statement-2 (R): For any positive real number $x: \sqrt{x \sqrt{x \sqrt{x \sqrt{x \sqrt{x}}}}} \ldots x=x$.
- A
Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1
- B
Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1
- C
Statement-1 is True, Statement-2 is False
- D
Statement-1 is False, Statement-2 is True
View full solution →Statement-1 (A): $\sqrt{7 \sqrt{7 \sqrt{7 \sqrt{7}}}}=\sqrt[16]{7^{15}}$.
Statement-2 (R): $\sqrt{a \sqrt{a \sqrt{a \ldots \ldots \ldots .}}} n$ terms $=a^{\frac{2^n-1}{2^n}}$.
- ✓
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- B
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- C
Statement-1 is true, Statement-2 is false.
- D
Statement-1 is false, Statement-2 is true.
Answer: A.
View full solution →Statement-1 (A): $\sqrt{6+\sqrt{6+\sqrt{6+\sqrt{6+}}}} \ldots \ldots \ldots \ldots \infty=3$.
Statement-2 (R): $\sqrt{x+\sqrt{x+\sqrt{x+}}} \ldots \ldots \ldots \ldots \infty=x, x>0$.
- A
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- B
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- ✓
Statement-1 is true, Statement-2 is false.
- D
Statement-1 is false, Statement-2 is true.
Answer: C.
View full solution →Statement-1 (A): $\sqrt{5 \sqrt{5 \sqrt{5 \sqrt{5}}}} \cdots \cdots \ldots \ldots=5 \sqrt{5}$.
Statement-2 (R): $\sqrt{x \sqrt{x \sqrt{x \sqrt{x}}}} \ldots \ldots \ldots \ldots \infty=x, x>0$.
- A
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- B
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- C
Statement-1 is true, Statement-2 is false.
- ✓
Statement-1 is false, Statement-2 is true.
Answer: D.
View full solution →Statement-1 (A): $\left[\left\{\left(\frac{1}{7^2}\right)^{-2}\right\}^{-1 / 3}\right]^{1 / 4}=7^{-1 / 3}$
Statement-2 (R): $\left(\left(a^m\right)^n\right)^s=a^{m n s}, a>0$
- ✓
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- B
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- C
Statement-1 is true, Statement-2 is false.
- D
Statement-1 is false, Statement-2 is true.
Answer: A.
View full solution →The value of $4 \times(256)^{-1 / 4} \div(243)^{1 / 5}$ is _______________ .
View full solution →The value of $(256)^{0.16} \times(256)^{0.09}$ is _______________ .
View full solution →The product $\sqrt[3]{2} \cdot \sqrt[4]{2} \cdot \sqrt[12]{32}$ is equal to _______________ .
View full solution →$\sqrt[4]{\sqrt[3]{2^2}}$ equals _______________ .
View full solution →$\sqrt[4]{(81)^{-2}}$ is equal $t$ _______________ .
View full solution →Write the value of $\sqrt[3]{7} \times \sqrt[3]{49}$
View full solution →Write the value of $\sqrt[3]{125 \times 27}$
View full solution →Write the value of $\left\{5\left(8^{1 / 3}+27^{1 / 3}\right)^3\right\}^{1 / 4}$.
View full solution →Write $\left(\frac{1}{9}\right)^{-1 / 2} \times(64)^{-1 / 3}$ as a rational number.
View full solution →Write $(625)^{-1 / 4}$ in decimal form.
View full solution →Write the value of $\sqrt[3]{7}\times\sqrt[3]{49}.$
View full solution →Write the value of $\sqrt[3]{125\times27}.$
View full solution →Write $\Big(\frac{1}{9}\Big)^{-\frac{1}{2}}\times(64)^{-\frac{1}{3}}$ as a rational number.
View full solution →Write $(625)^{-\frac{1}{4}}$ in decimal form.
View full solution →State the power law of exponents.
Write the value of $\Big\{5\Big(8^{\frac{1}{3}}+27^{\frac{1}{3}}\Big)^3\Big\}^{\frac{1}{4}}.$
View full solution →State the product law of exponents.
If $3^\text{x}=5^\text{y}=(75^\text{z}),$ show that $\text{z}=\frac{\text{xy}}{2\text{x}+\text{y}}.$
View full solution →Solve the following equations:
$4^{2\text{x}}=(\sqrt[3]{16})^{\frac{-6}{\text{y}}}=(\sqrt{8})^2$
View full solution →Solve the following equations for x:
$3^{2\text{x}+4}+1=2\times3^{\text{x}+2}$
View full solution →Solve the following equations:
$8^{\text{x}+1}=16^{\text{y}+2}$ and $\Big(\frac{1}{2}\Big)^{3+\text{x}}=\Big(\frac{1}{4}\Big)^{3\text{y}}$
View full solution →Simplify:
$\Big(\frac{\text{x}^{\text{a}+\text{b}}}{\text{x}^\text{c}}\Big)^{\text{a}-\text{b}}\Big(\frac{\text{x}^{\text{b}+\text{c}}}{\text{x}^\text{a}}\Big)^{\text{b}-\text{c}}\Big(\frac{\text{x}^{\text{c}+\text{a}}}{\text{x}^\text{b}}\Big)^{\text{c}-\text{a}}$
View full solution →Simplify: $\sqrt[\text{lm}]{\frac{\text{x}^\text{l}}{\text{x}^\text{m}}}\times\sqrt[\text{mn}]{\frac{\text{x}^\text{m}}{\text{x}^\text{n}}}\times\sqrt[\text{nl}]{\frac{\text{x}^\text{n}}{\text{x}^\text{l}}}$
View full solution →Simplify $\Big[\Big\{(625)^{\frac{1}{2}}\Big\}^{-\frac{1}{4}}\Big]^2$
View full solution →Prove that:
$\Big(\frac{1}{4}\Big)^{-2}-3\times8^{\frac{2}{3}}\times4^0+\Big(\frac{9}{16}\Big)^{-\frac{1}{2}}=\frac{16}{3}$
View full solution →