What is (5rs^4tu)(3r^2s^9t^7u) ?

The solution to (5rs^4tu)(3r^2s^9t^7u) is 15r^3s^{13}t^8u^2

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simplify (5rs^4tu)(3r^2s^9t^7u)

simplify

(5 r s^{4} t u) (3 r^{2} s^{9} t^{7} u)

15 r^{3} s^{13} t^{8} u^{2}

Solution steps

(5 r s^{4} t u) (3 r^{2} s^{9} t^{7} u)

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

r r^{2} = r^{1 + 2}

= 5 s^{4} t u \cdot 3 r^{1 + 2} s^{9} t^{7} u

Add the numbers:

1 + 2 = 3

= 5 s^{4} t u \cdot 3 r^{3} s^{9} t^{7} u

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

s^{4} s^{9} = s^{4 + 9}

= 5 t u \cdot 3 r^{3} s^{4 + 9} t^{7} u

Add the numbers:

4 + 9 = 13

= 5 t u \cdot 3 r^{3} s^{13} t^{7} u

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

t t^{7} = t^{1 + 7}

= 5 u \cdot 3 r^{3} s^{13} t^{1 + 7} u

Add the numbers:

1 + 7 = 8

= 5 u \cdot 3 r^{3} s^{13} t^{8} u

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

uu = u^{1 + 1}

= 5 \cdot 3 r^{3} s^{13} t^{8} u^{1 + 1}

Add the numbers:

1 + 1 = 2

= 5 \cdot 3 r^{3} s^{13} t^{8} u^{2}

Multiply the numbers:

5 \cdot 3 = 15

= 15 r^{3} s^{13} t^{8} u^{2}

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What is (5rs^4tu)(3r^2s^9t^7u) ?
The solution to (5rs^4tu)(3r^2s^9t^7u) is 15r^3s^{13}t^8u^2