Question

For what value of a does (one-ninth) superscript a 1 baseline = 81 superscript a 1 baseline times 27 superscript 2 minus a?

Answer 1

The value of a is a=-4 for

What is an exponent?

⇒An exponent refers to the number of times a number is multiplied by itself.

Multiplication of exponents

⇒ It is also known as the law on indices. For multiplication with the same base, we add the powers.

For the same base $a^{m}\times a^{n}$ = $a^{m+n}$

$(a^{m}) ^{n}$ = $a^{mn}$

Calculation :

We have been given that $(\frac{1}{9}) ^{a+1} } =81^{a+1} \times27^{2-a}$  ------------------(1)

To solve this equation we are going to make the bases equal

we need to take note that 9 = 3² , 81 = 3⁴ and 27 =3³

Now, we are going to replace 9, 81, and 27 by  3², 3⁴, and 3³ respectively in equation(1)

$(\frac{1}{3^{2} }) ^{a+1} } =(3^4)^{a+1} \times(3^3)^{2-a}$------------------- (2)

Also $\frac{1}{3^{2} }=3^{-2}$

We are going to replace $\frac{1}{3^{2} }$ by $3^{-2}$ in equation (2)

$({3^{-2} }) ^{a+1} } =(3^4)^{a+1} \times(3^3)^{2-a}$

On opening the parenthesis and applying the law of indices

$3^ ^{-2a-21} } =3^{4a+4} \times(3)^{6-3a}$

On the right-hand side of the equation, we will apply the law of indices for the same base which states that $a^{m}\times a^{n}$=$a^{m+n}$

⇒ $3^ ^{-2a-2} } =3^{4a+4+6-3a}$

The 3 on the left-hand side will cancel out the 3 on the right-hand side leaving us with just the powers

-2a - 2 = 4a + 4 + 6 - 3a

-2a - 2 = 4a + 10 - 3a

-2a - 4a + 3a = 10 + 2

-6a + 3a = 12

-3a = 12

a=-3

Therefore, the value of a is -4

Learn more about the law of indices here :

brainly.com/question/170984

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Questions : For what value of a does (one-ninth) Superscript a + 1 Baseline = 81 Superscript a + 1 Baseline times 27 Superscript 2 minus a?