Algebra Examples

$(8 b^{\frac{2}{3}} \cdot 9 t^{\frac{1}{5}}) (8 b^{\frac{5}{3}} \cdot 9 t^{\frac{3}{5}})$

Step 1

Multiply $b^{\frac{2}{3}}$ by $b^{\frac{5}{3}}$ by adding the exponents.

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Step 1.1

Move $b^{\frac{5}{3}}$ .

$8 (b^{\frac{5}{3}} b^{\frac{2}{3}}) \cdot (9 t^{\frac{1}{5}}) (8 \cdot (9 t^{\frac{3}{5}}))$

Step 1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$8 b^{\frac{5}{3} + \frac{2}{3}} \cdot (9 t^{\frac{1}{5}}) (8 \cdot (9 t^{\frac{3}{5}}))$

Step 1.3

Combine the numerators over the common denominator.

$8 b^{\frac{5 + 2}{3}} \cdot (9 t^{\frac{1}{5}}) (8 \cdot (9 t^{\frac{3}{5}}))$

Step 1.4

Add $5$ and $2$ .

$8 b^{\frac{7}{3}} \cdot (9 t^{\frac{1}{5}}) (8 \cdot (9 t^{\frac{3}{5}}))$

Step 2

Multiply $t^{\frac{1}{5}}$ by $t^{\frac{3}{5}}$ by adding the exponents.

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Step 2.1

Move $t^{\frac{3}{5}}$ .

$8 b^{\frac{7}{3}} \cdot (9 (t^{\frac{3}{5}} t^{\frac{1}{5}})) (8 \cdot (9))$

Step 2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$8 b^{\frac{7}{3}} \cdot (9 t^{\frac{3}{5} + \frac{1}{5}}) (8 \cdot (9))$

Step 2.3

Combine the numerators over the common denominator.

$8 b^{\frac{7}{3}} \cdot (9 t^{\frac{3 + 1}{5}}) (8 \cdot (9))$

Step 2.4

Add $3$ and $1$ .

$8 b^{\frac{7}{3}} \cdot (9 t^{\frac{4}{5}}) (8 \cdot (9))$

Step 3

Rewrite using the commutative property of multiplication.

$8 \cdot 9 b^{\frac{7}{3}} t^{\frac{4}{5}} (8 \cdot (9))$

Step 4

Multiply $8$ by $9$ .

$72 b^{\frac{7}{3}} t^{\frac{4}{5}} (8 \cdot (9))$

Step 5

Multiply $8$ by $9$ .

$72 b^{\frac{7}{3}} t^{\frac{4}{5}} \cdot 72$

Step 6

Multiply $72$ by $72$ .

$5184 b^{\frac{7}{3}} t^{\frac{4}{5}}$