Rewrite each expression as a single power (-4)⁶(-4)⁵ 13⁷x 13² 9¹⁴/9⁷ (-24)⁵/-24

Mathematics

2 answers:

professor190 [17]3 years ago

4 0

Step-by-step explanation:

(-4)^11,13^9,9^7,(-24)^4

BabaBlast [244]3 years ago

3 0

1. -4^11
2. 13^9
3. 9^7
4. -24^4

You might be interested in

Two numbers have a difference of 24. What is the sum of their squares if it is a minimum?

seraphim [82]

Let "a" and "b" be some number where:

a - b = 24

We want to find where a^2 + b^2 is a minimum. Instead of just logically figuring out that the answer is where a=b=12, I'll just use derivatives.

So we can first substitute for "a" where a = b+24

So we have (b+24)^2 + b^2 = b^2 +48b +576 + b^2
And that equals 2b^2 +48b +576

Then we take the derivative and set it equal to zero:

4b +48 = 0
4(b+12) = 0
b + 12 = 0
b = -12

Thus "a" must equal 12.

So:
a = 12
b = -12

And the sum of those two numbers squared is (12)^2 + (-12)^2 = 144 + 144 = 288.

The smallest sum is 288.

3 0

3 years ago

If the line joining (3x, x+1) and (11,12) has a slope of 4 what is the value of x

Irina18 [472]

Answer:

x = 3

Step-by-step explanation:

$(3x,\: x +1)=(x_1, \:y_1)$

$(11,\: 12)=(x_2, \:y_2)$

$slope = \frac{y_2 - y_1}{x_2 - x_1} \\ \\ 4 = \frac{12 - (x + 1)}{11 - 3x} \\ \\ 4 = \frac{12 - x - 1}{11 - 3x} \\ \\ 4 = \frac{11 - x}{11 - 3x} \\ \\ 4(11 - 3x) = 11 - x \\ \\ 44 - 12x = 11 - x \\ \\ 44 - 11 = 12x - x \\ \\ 33 = 11x \\ \\ x = \frac{33}{11} \\ \\ \huge \red{ \boxed{x = 3}}$