Question

Please help me match them all​

Answer 1

Step-by-step explanation:

Step 1:  Match the questions

1.  Dividing the same base → $\frac{x^7}{x^3}$ is an example of this and to divide exponents (or powers) with the same base, subtract the exponents.  Therefore we match this with option E

2.  Negative exponent with a fraction base → $(3)^{-3}$ is an example of this and in other words, the negative exponent rule tells us that a number with a negative exponent should be put to the denominator, and vice versa.  Therefore we match this with option H

3.  Product to a Power → $(2x)^3$ is an example of this and what we do is basically distribute out the exponent to everything inside of the parenthesis.  Therefore we match this with option B

4.  Power of 0 → $(15)^0$ is an example of this and what we do is basically say that the exponent of a number shows how many times the number is multiplied by itself. The zero property of exponents is applied when the exponent of any base is 0.  Therefore we match this with option C

5.  Negative exponent → $(\frac{3}{10})^{-4}$ is an example of this and a negative exponent is defined as the multiplicative inverse of the base, raised to the power which is opposite to the given power. In simple words, we write the reciprocal of the number and then solve it like positive exponents.  Therefore we match this with option G

6.  Power to a Power → $(x^2)^2$ is an example of this and what we do is multiply the powers by each other by doing $(x^{2*2})$ which would give us $x^4$.  Therefore we match this with option A

7.  Multiplying the same base → $x^5*x^3$ is an example of this and according to the exponent rule for multiplication with the same base, we simply add the powers.  Therefore we match this with option D

8.  Quotient to a Power → $(\frac{a}{b})^x$ is an example of this and when you raise a quotient to a power you raise both the numerator and the denominator to the power.  Therefore we match this with option F