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mr Goodwill [35]
3 years ago
10

Write (8a^-3)^-4/3 in simplest form. Please show your work!

Mathematics
2 answers:
german3 years ago
8 0

Answer:

(a/2) ^4  or a^4/16

Step-by-step explanation:

(8a^-3)^-4/3

split into two parts

8^ -4/3   *  (a^-3)^-4/3

using the power to the power rule we can multiply the exponents

8^(-4/3)  *a^(-3*-4/3)

8^ (-4/3) * a^(4)

replace 8 with 2^3

(2^3)^(-4/3) * a^(4)

using the power to the power rule we can multiply the exponents

2^(3*-4/3) * a^(4)

2 ^ (-4) * a^4

the negative exponent means it goes in the denominator if it is in the numerator

a^4/2^4

make a fraction

(a/2) ^4

or a^2/16

11111nata11111 [884]3 years ago
3 0

Answer:

\frac{a^4}{16}

Step-by-step explanation:

(8a^{-3})^\frac{-4}{3}

To simplify it we apply exponential property

(a^m)^n= a^mn

we multiply the inside exponent with outside exponent

8 or 8^1  are same

(8^1a^{-3})^\frac{-4}{3}

(8^{1 \cdot \frac{-4}{3}}a^{-3 \cdot \frac{-4}{3}})

When we multiply the exponents we get

8^{\frac{-4}{3}}a^{4}

8 can be written as 2 times 2 times 2 is 2^3

2^{3 \cdot {\frac{-4}{3}}}a^{4}

2^{-4}a^4

Now to make exponent positive move a^-4 to the denominator

\frac{a^4}{2^4}

\frac{a^4}{16}

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