Simplify (y^3z^-5)^(23/30)(y^4)^6

${(y^{3} z^{- 5})}^{\frac{23}{30}} {(y^{4})}^{6}$

Step 1

Rewrite the expression using the negative exponent rule

$b^{- n} = \frac{1}{b^{n}}$ .

${(y^{3} \frac{1}{z^{5}})}^{\frac{23}{30}} {(y^{4})}^{6}$

Step 2

Combine

$y^{3}$ and

$\frac{1}{z^{5}}$ .

${(\frac{y^{3}}{z^{5}})}^{\frac{23}{30}} {(y^{4})}^{6}$

Step 3

Apply basic rules of exponents.

Apply the product rule to

$\frac{y^{3}}{z^{5}}$ .

$\frac{{(y^{3})}^{\frac{23}{30}}}{{(z^{5})}^{\frac{23}{30}}} {(y^{4})}^{6}$

Multiply the exponents in

${(y^{3})}^{\frac{23}{30}}$ .

Apply the power rule and multiply exponents,

${(a^{m})}^{n} = a^{m n}$ .

$\frac{y^{3 (\frac{23}{30})}}{{(z^{5})}^{\frac{23}{30}}} {(y^{4})}^{6}$

Cancel the common factor of

$3$ .

Factor

$3$ out of

$30$ .

$\frac{y^{3 \frac{23}{3 (10)}}}{{(z^{5})}^{\frac{23}{30}}} {(y^{4})}^{6}$

Cancel the common factor.

$\frac{y^{3 \frac{23}{3 \cdot 10}}}{{(z^{5})}^{\frac{23}{30}}} {(y^{4})}^{6}$

Rewrite the expression.

$\frac{y^{\frac{23}{10}}}{{(z^{5})}^{\frac{23}{30}}} {(y^{4})}^{6}$

Multiply the exponents in

${(z^{5})}^{\frac{23}{30}}$ .

Apply the power rule and multiply exponents,

${(a^{m})}^{n} = a^{m n}$ .

$\frac{y^{\frac{23}{10}}}{z^{5 (\frac{23}{30})}} {(y^{4})}^{6}$

Cancel the common factor of

$5$ .

Factor

$5$ out of

$30$ .

$\frac{y^{\frac{23}{10}}}{z^{5 \frac{23}{5 (6)}}} {(y^{4})}^{6}$

Cancel the common factor.

$\frac{y^{\frac{23}{10}}}{z^{5 \frac{23}{5 \cdot 6}}} {(y^{4})}^{6}$

Rewrite the expression.

$\frac{y^{\frac{23}{10}}}{z^{\frac{23}{6}}} {(y^{4})}^{6}$

Multiply the exponents in

${(y^{4})}^{6}$ .

Apply the power rule and multiply exponents,

${(a^{m})}^{n} = a^{m n}$ .

$\frac{y^{\frac{23}{10}}}{z^{\frac{23}{6}}} y^{4 \cdot 6}$

Multiply

$4$ by

$6$ .

$\frac{y^{\frac{23}{10}}}{z^{\frac{23}{6}}} y^{24}$

Step 4

Multiply

$\frac{y^{\frac{23}{10}}}{z^{\frac{23}{6}}} y^{24}$ .

Combine

$\frac{y^{\frac{23}{10}}}{z^{\frac{23}{6}}}$ and

$y^{24}$ .

$\frac{y^{\frac{23}{10}} y^{24}}{z^{\frac{23}{6}}}$

Multiply

$y^{\frac{23}{10}}$ by

$y^{24}$ by adding the exponents.

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{y^{\frac{23}{10} + 24}}{z^{\frac{23}{6}}}$

To write

$24$ as a fraction with a common denominator, multiply by

$\frac{10}{10}$ .

$\frac{y^{\frac{23}{10} + 24 \cdot \frac{10}{10}}}{z^{\frac{23}{6}}}$

Combine

$24$ and

$\frac{10}{10}$ .

$\frac{y^{\frac{23}{10} + \frac{24 \cdot 10}{10}}}{z^{\frac{23}{6}}}$

Combine the numerators over the common denominator.

$\frac{y^{\frac{23 + 24 \cdot 10}{10}}}{z^{\frac{23}{6}}}$

Simplify the numerator.

Multiply

$24$ by

$10$ .

$\frac{y^{\frac{23 + 240}{10}}}{z^{\frac{23}{6}}}$

Add

$23$ and

$240$ .

$\frac{y^{\frac{263}{10}}}{z^{\frac{23}{6}}}$

Simplify (y^3z^-5)^(23/30)(y^4)^6

Related Questions