Step-by-step explanation:
1)
x⁴×x^a = x¹²
you know that you can add the exponents when multiplying terms with the same base value/variable ?
because that is what we are doing here to solve it :
x^(4 + a) = x¹²
therefore,
4 + a = 12
a = 8
2)
y^b / y⁵ = y²
similar to 1), but when we divide, we subtract the exponents.
y^(b - 5) = y²
b - 5 = 2
b = 7
3)
3^c = 1/27
27 = 3³
27×3^c = 1
3³×3^c = 1
3^(3 + c) = 1
now we need to remember : x⁰ = 1.
therefore, 3⁰ = 1
3^(3 + c) = 3⁰
3 + c = 0
c = -3
4)
(m³)² = m^d
aha !
now we need to remember, we can multiply the exponents, when we have an exponent of an exponent term.
m^(3×2) = m^d
3×2 = d
6 = d
5)
7⁰ = e
remember, x⁰ = 1, so also 7⁰ = 1.
therefore, e = 1.
6)
4^-2 × 4⁹ × 4^‐5 = 4^f
so, now we need apply what we just learned to a sequence of operations :
each term has the same base value (4), and they are all multiplied, so we can do the described adding of the exponents :
4^(-2 + 9 - 5) = 4^f
therefore,
f = -2 + 9 - 5 = 2
