1. (5^5) * (5^6) - This is equal to 5 raised to the 5th power multiplied by 5 raised to the 6th power, which equals 5 raised to the 11th power because when you multiply two powers with the same base, you add their exponents.
2. (5^10) * (5^1) - This is equal to 5 raised to the 10th power multiplied by 5 raised to the 1st power, which also equals 5 raised to the 11th power because, as mentioned before, adding the exponents of two powers with the same base gives you the result of multiplying those two powers.
3. (5^3) * (5^3) * (5^3) * (5^2) - This is equal to 5 raised to the 3rd power multiplied by itself three times, and then multiplied by 5 raised to the 2nd power. This equals 5 raised to the 11th power because when you multiply multiple powers with the same base, you add their exponents, which in this case would be 3+3+3+2=11.
All three expressions are equivalent to 5^11 because they are just different ways of expressing the same value. By using the laws of exponents, which state that multiplying two powers with the same base is equivalent to adding their exponents, we can see that all three expressions result in multiplying different combinations of factors that when combined, equal 5 raised to the 11th power.
10.
List three different ways to write 5^11
as the product of two powers. Explain why all three of
your expressions are equal to 5^11
1 answer