Question

Rules for multiplying exponents

Answer 1

Answer and Step-by-step explanation:

When multiplying exponents:

- Product of Powers: When the base of the exponents are the same, and the bases are being multiplied to each other, the exponents are added together.

Example: $a^x + a^y = a^{x+y}$

- Different bases Same Exponents: When the bases of the exponents are different, but the exponents are the same, the bases multiply together (within a parenthesis) with the exponent on the parenthesis.

Example: $a^x*b^x = (a*b)^x$

- Quotient of Powers: When the base of the exponents are the same, and they are being divided by each other, the exponents will subtract from each other.

Example: $\frac{a^x}{a^y}= a^{x-y}$

- Power of a Power: When a base has an exponent, and that entire term has and exponent, the exponents multiply together.

Example: $(a^x)^y = a^{x*y}$

- Power of a Product: The opposite of Different bases Same Exponents. Distribute the exponent onto the different bases.

Example: $(ab)^x = a^x*b^x$

- Power of a Quotient: The opposite of Quotient of Powers. Distribute the exponent to the dividing bases.

Example: $(\frac{a}{b} )^x = \frac{a^x}{b^x}$

- Zero Power: Any number raised to the 0 power equals 1.

Example: $a^0 = 1\\999999^0=1$

- Negative Exponent: Any number raised by a negative number goes to the denominator of a fraction (if not already in the denominator), and vise versa (goes to the numerator if not already in the numerator).

Example: $a^-2 = \frac{1}{a^2} \\\\\frac{1}{b^-3} = b^3$

- Power of One: Any number raised to the power of 1 is the same number.

Example: $a^1 = a\\\\999^1 = 999$

I hope this helps!

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