Answer:
7) y⁹
9) a⁸
Step-by-step explanation:
when we multiply two exponents (of the same base), we can add them
so, a² · a³ = a² ⁺ ³ = a⁵
let's test it out!
(a = 2 in our example)
2² · 2³ = 2⁵
4 · 8 = 32 (2⁵ = 32)
32 = 32
because this is true, we know that we can add exponents of the same base when multiplying them together
now, let's try out the question at hand:
y³ · y⁶
well, we know that 3 + 6 = 9, so y³ · y⁶ can be simplified to y⁹
--
now, we're going to be working with division. We know that division is the inverse of multiplication, so we logically know that instead of adding exponents, we subtract them when dividing
here,
a³ ÷ a² would equal a¹ (3 - 2 = 1)
let's put a = 2 again:
a³ ÷ a² = a³ ⁻ ² = a¹ = a
2³ ÷ 2² = 2¹
8 ÷ 4 = 2
2 = 2
once again, we have proven this shortcut to be true
now, to the problem at hand!
first, we can multiply a³ · a⁹
a³ · a⁹ = a³ ⁺ ⁹ = a¹²
so, let's rewrite the problem:
a¹² / a⁴
because we're dividing with exponents, we can subtract 12 - 4
a¹² / a⁴
a¹² ÷ a⁴
a¹² ⁻ ⁴
a⁸
so, our simplified answer is a⁸
(note: they must be the same base, [the thing that the exponent is attached to] for this to apply)
hope this helps (and makes sense)! have a lovely day :)
