Algebra Examples

$t^{- \frac{5}{2}} = 32$

Step 1

Raise each side of the equation to the power of $- \frac{2}{5}$ to eliminate the fractional exponent on the left side.

${(t^{- \frac{5}{2}})}^{- \frac{2}{5}} = 32^{- \frac{2}{5}}$

Step 2

Simplify the exponent.

Tap for more steps...

Step 2.1

Simplify the left side.

Tap for more steps...

Step 2.1.1

Simplify ${(t^{- \frac{5}{2}})}^{- \frac{2}{5}}$ .

Tap for more steps...

Step 2.1.1.1

Multiply the exponents in ${(t^{- \frac{5}{2}})}^{- \frac{2}{5}}$ .

Tap for more steps...

Step 2.1.1.1.1

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

$t^{- \frac{5}{2} (- \frac{2}{5})} = 32^{- \frac{2}{5}}$

Step 2.1.1.1.2

Cancel the common factor of $5$ .

Tap for more steps...

Step 2.1.1.1.2.1

Move the leading negative in $- \frac{5}{2}$ into the numerator.

$t^{\frac{- 5}{2} (- \frac{2}{5})} = 32^{- \frac{2}{5}}$

Step 2.1.1.1.2.2

Move the leading negative in $- \frac{2}{5}$ into the numerator.

$t^{\frac{- 5}{2} \cdot \frac{- 2}{5}} = 32^{- \frac{2}{5}}$

Step 2.1.1.1.2.3

Factor $5$ out of $- 5$ .

$t^{\frac{5 (- 1)}{2} \cdot \frac{- 2}{5}} = 32^{- \frac{2}{5}}$

Step 2.1.1.1.2.4

Cancel the common factor.

$t^{\frac{5 \cdot - 1}{2} \cdot \frac{- 2}{5}} = 32^{- \frac{2}{5}}$

Step 2.1.1.1.2.5

Rewrite the expression.

$t^{\frac{- 1}{2} \cdot - 2} = 32^{- \frac{2}{5}}$

Step 2.1.1.1.3

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.1.1.1.3.1

Factor $2$ out of $- 2$ .

$t^{\frac{- 1}{2} \cdot (2 (- 1))} = 32^{- \frac{2}{5}}$

Step 2.1.1.1.3.2

Cancel the common factor.

$t^{\frac{- 1}{2} \cdot (2 \cdot - 1)} = 32^{- \frac{2}{5}}$

Step 2.1.1.1.3.3

Rewrite the expression.

$t^{- - 1} = 32^{- \frac{2}{5}}$

Step 2.1.1.1.4

Multiply $- 1$ by $- 1$ .

$t^{1} = 32^{- \frac{2}{5}}$

Step 2.1.1.2

Simplify.

$t = 32^{- \frac{2}{5}}$

Step 2.2

Simplify the right side.

Tap for more steps...

Step 2.2.1

Simplify $32^{- \frac{2}{5}}$ .

Tap for more steps...

Step 2.2.1.1

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

$t = \frac{1}{32^{\frac{2}{5}}}$

Step 2.2.1.2

Simplify the denominator.

Tap for more steps...

Step 2.2.1.2.1

Rewrite $32$ as $2^{5}$ .

$t = \frac{1}{{(2^{5})}^{\frac{2}{5}}}$

Step 2.2.1.2.2

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

$t = \frac{1}{2^{5 (\frac{2}{5})}}$

Step 2.2.1.2.3

Cancel the common factor of $5$ .

Tap for more steps...

Step 2.2.1.2.3.1

Cancel the common factor.

$t = \frac{1}{2^{5 (\frac{2}{5})}}$

Step 2.2.1.2.3.2

Rewrite the expression.

$t = \frac{1}{2^{2}}$

Step 2.2.1.2.4

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

$t = \frac{1}{4}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$t = \frac{1}{4}$

Decimal Form:

$t = 0.25$