Suppose you didn't know that b^0=1. Explain how you could arrive at this fact by using the laws of exponents to simplify b^2 times b^0=b^2

I am so confused
Please help me!!
Thanks

~aShLeY

by the rules of powers

(a^m)(a^n) = a^(m+n)

so suppose we multiply

a^m by a^0

by the above law,
a^m(a^0) = a^m

so we multiplied a^m by some value and we got back a^m, no change in value!

the only way this could have happened is that a^0 must have had a value of 1

okay, that makes sense, thanks so much

what is the value of the expression blow if a=4 and b=-4

Sure, I can help you understand how to arrive at the fact that b^0 is equal to 1 using the laws of exponents.

First, let's start with the equation b^2 * b^0 = b^2. We want to simplify this equation using the laws of exponents. One of the exponent laws states that when multiplying two powers with the same base, you add their exponents. So we can rewrite the equation as b^(2+0) = b^2.

Now, to simplify further, we need to understand what happens when we add 0 as an exponent. To do this, let's use another exponent law, which tells us that any number (except 0) raised to the power of 0 is equal to 1.

So, applying this law, we can rewrite the equation as b^2 * 1 = b^2. Since any number multiplied by 1 is equal to itself, we have b^2 = b^2.

Now, we can observe that both sides of the equation have the same base (b) and the same exponent (2). According to the property of equality, if two expressions are equal, their corresponding exponents must be equal. Therefore, b^2 = b^2 implies that the exponents 2 on both sides are equal.

So, to make the exponents equal, we introduce the concept of the "zero exponent." Since b^2 is equal to b^2, we can say that b^(2-2) = b^0.

Using another exponent law that states when dividing two powers with the same base, you subtract their exponents, we get b^(2-2) = b^0 simplifies to b^0 = 1.

Therefore, by using the laws of exponents and simplifying the equation step by step, we can conclude that b^0 is equal to 1.