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Softa [21]
3 years ago
15

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
Mathematics
2 answers:
grin007 [14]3 years ago
8 0

Answer:

-4

Step-by-step explanation:

symbolab.com baybee thats whats up

Natalka [10]3 years ago
4 0

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

collect like-term

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

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