Algebra Examples

${(5^{4} \cdot b^{- 10})}^{- 6}$

Step 1

Raise $5$ to the power of $4$ .

${(625 \cdot b^{- 10})}^{- 6}$

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(625 \cdot \frac{1}{b^{10}})}^{- 6}$

Step 3

Combine $625$ and $\frac{1}{b^{10}}$ .

${(\frac{625}{b^{10}})}^{- 6}$

Step 4

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{b^{10}}{625})}^{6}$

Step 5

Apply the product rule to $\frac{b^{10}}{625}$ .

$\frac{{(b^{10})}^{6}}{625^{6}}$

Step 6

Multiply the exponents in ${(b^{10})}^{6}$ .

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Step 6.1

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

$\frac{b^{10 \cdot 6}}{625^{6}}$

Step 6.2

Multiply $10$ by $6$ .

$\frac{b^{60}}{625^{6}}$

Step 7

Raise $625$ to the power of $6$ .

$\frac{b^{60}}{59604644775390600}$