Radicals and Exponents Evaluate each expression:

a)$\frac{\sqrt{132}}{\sqrt{3}}$

b)$\sqrt{3}\left\{2\right\}\sqrt{3}\left\{32\right\}$

c)$\sqrt{4}\left\{\frac{1}{4}\right\}\sqrt{4}\left\{\frac{1}{64}\right\}$

a)

b)

c)

Bevan Mcdonald
2021-01-08
Answered

Radicals and Exponents Evaluate each expression:

a)$\frac{\sqrt{132}}{\sqrt{3}}$

b)$\sqrt{3}\left\{2\right\}\sqrt{3}\left\{32\right\}$

c)$\sqrt{4}\left\{\frac{1}{4}\right\}\sqrt{4}\left\{\frac{1}{64}\right\}$

a)

b)

c)

You can still ask an expert for help

StrycharzT

Answered 2021-01-09
Author has **102** answers

a) Formula used:

Power of nth roots:

$\sqrt{n}\left\{\frac{a}{b}\right\}=\frac{\sqrt{n}\left\{a\right\}}{\sqrt{n}\left\{a\right\}}$

Where n is any positive integer and a and b are bases.

Calculation:

The given exponential expression is$\frac{\sqrt{132}}{\sqrt{3}}$

Use the above-mentioned formula and calculate the value of$\frac{\sqrt{132}}{\sqrt{3}}$ as shown below.

$\frac{\sqrt{132}}{\sqrt{3}}=\frac{\sqrt{11\cdot 2\cdot 2\cdot 3}}{\sqrt{3}}$

$=\frac{2\sqrt{11}\cdot \sqrt{3}}{\sqrt{3}}$

$=2\sqrt{11}$

Thus, the value of exponential is$2\sqrt{11}$

b) Calculation:

Use the above mentioned formula and simplify the given expression as shown below.

$\sqrt{3}\left\{2\right\}\sqrt{3}\left\{32\right\}=\sqrt{3}\left\{2\right\}\sqrt{3}\{2\cdot 2\cdot 2\cdot 2\cdot 2\}$

$={\left({2}^{6}\right)}^{\frac{1}{3}}$

$={2}^{2}$

$=4$

Thus, the value of exponential expression is 4.

c) Calculation:

$\sqrt{4}\left\{\frac{1}{4}\right\}\sqrt{4}\left\{\frac{1}{64}\right\}=\sqrt{4}\left\{\frac{1}{4}\right\}\sqrt{4}\left\{\frac{1}{4\cdot 4\cdot 4}\right\}$

$=\sqrt{4}\left\{\frac{1}{{\left(4\right)}^{4}}\right\}$

$=\frac{1}{{\left({4}^{4}\right)}^{\frac{1}{4}}}$

$=\frac{1}{4}$

The value of exponential is$\frac{1}{4}.$

Power of nth roots:

Where n is any positive integer and a and b are bases.

Calculation:

The given exponential expression is

Use the above-mentioned formula and calculate the value of

Thus, the value of exponential is

b) Calculation:

Use the above mentioned formula and simplify the given expression as shown below.

Thus, the value of exponential expression is 4.

c) Calculation:

The value of exponential is

Jeffrey Jordon

Answered 2021-10-27
Author has **2262** answers

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