Quotient of like bases: **To divide powers with the same base, subtract the exponents and keep the common base**. 3. Power to a power: To raise a power to a power, keep the base and multiply the exponents. … Zero exponent: Any number raised to the zero power is equal to “1”.

What are the 5 properties of exponents?

- Product of Powers.
- Power to a Power.
- Quotient of Powers.
- Power of a Product.
- Power of a Quotient.

What are the 7 properties of exponents?

- Product of powers rule. …
- Quotient of powers rule. …
- Power of a power rule. …
- Power of a product rule. …
- Power of a quotient rule. …
- Zero power rule. …
- Negative exponent rule.

What are the six properties of exponents?

- 1 Rule 1 (Product of Powers)
- 2 Rule 2 (Power to a Power)
- 3 Rule 3 (Multiple Power Rules)
- 4 Rule 4 (Quotient of Powers)
- 5 Rule 5 (Power of a quotient)
- 6 Rule 6 (Negative Exponents)
- 7 Quiz.

## What are the properties of exponents and powers?

When you raise a quotient to a power you **raise both the numerator and the denominator to the power**. When you raise a number to a zero power you’ll always get 1. Negative exponents are the reciprocals of the positive exponents. The same properties of exponents apply for both positive and negative exponents.

## What is the formula for a m a n?

**am * an = a(m+n)** says that when you take a number, a, multiplied by itself m times, and multiply that by the same number a multiplied by itself n times, it’s the same as taking that number a and raising it to a power equal to the sum of m + n. 2.

## What are the 8 laws of exponents?

- Multiplying Powers with same Base.
- Dividing Powers with the same Base.
- Power of a Power.
- Multiplying Powers with the same Exponents.
- Negative Exponents.
- Power with Exponent Zero.
- Fractional Exponent.

## What is the one to one property of exponents?

Recall that the one-to-one property of exponential functions tells us that, for any real numbers b, S, and T, where b>0, b≠1 b > 0 , b ≠ 1 , **bS=bT b S = b T if** and only if S = T. In other words, when an exponential equation has the same base on each side, the exponents must be equal.

## What are exponent rules?

The Power Rule for Exponents: **(am)n = am*n**. To raise a number with an exponent to a power, multiply the exponent times the power. Negative Exponent Rule: x–n = 1/xn. Invert the base to change a negative exponent into a positive.

## What is the quotient rule for exponents?

Quotient Rule of Exponents When **dividing exponential expressions that have the same base, subtract the exponents**.

## What are the properties of exponential equations?

Exponential equations are equations **in which variables occur as exponents**. For example, exponential equations are in the form ax=by . To solve exponential equations with same base, use the property of equality of exponential functions . If b is a positive number other than 1 , then bx=by if and only if x=y .

## What are the properties of exponents Algebra 2?

Properties of Exponents: For all nonzero real numbers a and b and integers m and n , Words Numbers Algebra Product of Powers Property: **To multiply powers with the same base, add the exponents**. Quotient of Powers Property: To divide powers with the same base, subtract the exponents.

## What are the properties of exponents with examples?

Property | Example |
---|---|

( x n ) m = x n ⋅ m \left(x^n\right)^m=x^{n\cdot m} (xn)m=xn⋅m | ( 5 4 ) 3 = 5 12 \left(5^4\right)^3=5^{12} (54)3=512 |

( x ⋅ y ) n = x n ⋅ y n (x\cdot y)^n=x^n\cdot y^n (x⋅y)n=xn⋅yn | ( 3 ⋅ 5 ) 7 = 3 7 ⋅ 5 7 (3\cdot 5)^7=3^7\cdot 5^7 (3⋅5)7=37⋅57 |

## What is properties of equality?

Two equations that have **the same** solution are called equivalent equations e.g. 5 +3 = 2 + 6. As well as it goes for the multiplication property of equality. … If you multiply each side of an equation with the same nonzero number you produce an equivalent equation.