List three different ways to write [tex]5^{11}[/tex] as the product of two powers. Explain why all three of your expressions are equal to [tex]5^{11}[/tex].

1. [tex]5^{4} \times 5^{7} = 5^{11}[/tex]
2. [tex]5^{5} \times 5^{6} = 5^{11}[/tex]
3. [tex]5^{3} \times 5^{8} = 5^{11}[/tex]

All three expressions are equal to [tex]5^{11}[/tex] because when multiplying powers with the same base, you add the exponents.

when multiplying a number to a power, you add the powers.
for example 5^3 x 5^8 = 5^11
you can do the same with 2&9, 4&7, 5&6

Answered by kayt91 | 2024-06-10

ok i got it its 5^1 5^3 5^8 and 5^10 lol yw

Answered by mjchey | 2024-06-10

We can express 5 11 as the product of two powers in several ways, such as 5 4 × 5 7 , 5 5 × 5 6 , and 5 3 × 5 8 . All these expressions equal 5 11 because adding the exponents results in 11. This is due to the rule of exponents that states when multiplying powers with the same base, we add the exponents.
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Answered by kayt91 | 2024-10-10