Pre-Algebra Examples

${(- 64)}^{\frac{2}{3}} + {(25)}^{\frac{3}{2}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $- 64$ as ${(- 4)}^{3}$ .

${({(- 4)}^{3})}^{\frac{2}{3}} + {(25)}^{\frac{3}{2}}$

Step 1.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(- 4)}^{3 (\frac{2}{3})} + {(25)}^{\frac{3}{2}}$

Step 1.3

Cancel the common factor of $3$ .

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Step 1.3.1

Cancel the common factor.

${(- 4)}^{3 (\frac{2}{3})} + {(25)}^{\frac{3}{2}}$

Step 1.3.2

Rewrite the expression.

${(- 4)}^{2} + {(25)}^{\frac{3}{2}}$

Step 1.4

Raise $- 4$ to the power of $2$ .

$16 + {(25)}^{\frac{3}{2}}$

Step 1.5

Rewrite $25$ as $5^{2}$ .

$16 + {(5^{2})}^{\frac{3}{2}}$

Step 1.6

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$16 + 5^{2 (\frac{3}{2})}$

Step 1.7

Cancel the common factor of $2$ .

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Step 1.7.1

Cancel the common factor.

$16 + 5^{2 (\frac{3}{2})}$

Step 1.7.2

Rewrite the expression.

$16 + 5^{3}$

Step 1.8

Raise $5$ to the power of $3$ .

$16 + 125$

Step 2

Add $16$ and $125$ .

$141$