Question

For what value of a does (one-ninth) Superscript a + 1 Baseline = 81 Superscript a + 1 Baseline times 27 Superscript 2 minus a? –4 –2 2 6

Answer 1

Answer:

-4

Step-by-step explanation:

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Answer 2

Answer:

The value of a is -4

Step-by-step explanation:

$(\frac{1}{9}) ^{a+1}$ =  $81^{a+1}$  ×  $27^{2-a}$  ------------------------------------(1)

No solve this, we need to take note that 9 = 3² , 81 = $3^{4}$     and 27 = $3^{3}$

Now, we are going to replace 9 , 81 and 27 by  3²,  $3^{4}$  and $3^{3}$ respectively in equation(1)

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

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

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

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

We can now open the parenthesis

$3^{-2a-2}$  =  $3^{4a + 4}$  ×  $3^{6-3a}$

At the right-hand side of the equation, we will apply the law of indices that state  $x^{a}$ × $x^{b}$  =  $x^{a+b}$  

This implies we will take just 3 and then add-up all the powers

$3^{-2a-2}$  = $3^{4a + 4+ 6-3a}$

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

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Which means we will take all the digits with variable to the left-hand side and then take all the digits standing alone to the right-hand side of the equation

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

-6a + 3a = 12

-3a = 12

Divide both-side of the equation by -3

$\frac{-3a}{-3}$ = $\frac{12}{-3}$

a = -4

Therefore, the value of a is -4