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User Kenia
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1 Answer

13 votes
13 votes

Answer:

1)

a=3

2)


(1)/(27)

Explanation:

Use the property of exponent,
a^m\cdot a^n=a^(m+n)


\left((2)/(3)\right)^(-3+8)=\left((2)/(3)\right)^(2a-1)

If
a^m=a^n then
m=n


-3+8=2a-1\\2a=5+1\\a=(6)/(2)\\a=3

b)


$(6^(4) * 9^(-2) * 25)/(2^(4) * 5^(2) * 3^(3))$=$((2*3)^(4) * 9^(-2) * 5^2)/(2^(4) * 5^(2) * 3^(3))$\\=( 2^4* 3^4* 9^(-2) )/(2^(4) * 3^(3))\\=( 3^4* 9^(-2) )/(3^(3))

Use the property of exponent,
(a^m)/(a^n)=a^(m-n)


=3^(4-3)* 9^(-2)\\=3* 9^(-2)

Use the property of exponent,
a^(-n)=(1)/(a^n)


=3* (1)/(9^2)\\=3* (1)/(81)\\= (1)/(27)

User Ashish Ranjan
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