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Mice21 [21]
3 years ago
6

What equivalent expression is equal to this(2^-4*2^-3)^5

Mathematics
1 answer:
Katen [24]3 years ago
8 0

(2^{-4} \cdot z^{-3})^5=2^{-4 \cdot 5} \cdot z^{-3 \cdot 5}=2^{-20} \cdot z^{-15}

⇒ \frac{1}{2^{20} \cdot z^{15}}


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podryga [215]

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1. k=13

2. x=-10

EXPLANATION

The given function is

f(x) =  {x}^{2}   + 3x  - 10

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This implies that:

f(x) =  {(x + 5)}^{2}   + 3(x + 5) - 10

Expand:

f(x) =   {x}^{2}    + 10x + 25+ 3x + 15- 10

Simplify to obtain

f(x) =   {x}^{2}    + 13x + 30

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f(x) =   {x}^{2}    + kx + 30

This implies that:

k = 13

To find the smallest zero of f(x+5), we equate the function to zero and solve for x.

{x}^{2}    + 13x + 30 = 0

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(x + 3)(x + 10) = 0

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