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Multiplication Property of Exponents

We can extend the Multiplication Property of Exponents to multiply more than two factors.

Example 1

Find: 8⁴ Â· 8 Â· 8⁵. Leave your answer in exponential notation.

Solution

The bases are the same, so we can use the Multiplication Property of Exponents.

Note: 8 = 8¹

8⁴ Â· 8 Â· 8⁵ = 8⁴ Â· 8¹ Â· 8⁵ = 8^{4 + 1 + 5} = 8¹⁰

We left 8¹⁰ in exponential form. To evaluate 8¹⁰, use the â€œy^xâ€ key on a scientific calculator or the â€œ^â€ key on a graphing calculator.

8¹⁰= 1,073,741,824

Example 2

Find: x⁷ Â· x³ Â· x⁵

Solution

The operation is multiplication and the bases are the same.

Therefore, add the exponents and use x as the base. x⁷ Â· x³ Â· x⁵ = x^{7 + 3 + 5} = x¹⁵