Video Transcript
Find the value of seven squared plus four times two to the power three in the
simplest form.
We’re given an expression involving integer exponents and asked to find its value in
the simplest form. To do this, we first recall the BIDMAS, BODMAS, or, equivalently in the US, PEMDAS
order of operations. In our case, we have an addition, a multiplication, and two indices or powers. And since the first of these operations to appear in our order of operations is
indices, we begin by expanding the two indices or powers.
To do this, we recall that for a power with a base 𝑎, where 𝑎 is a real number
excluding zero, and an integer exponent 𝑛, 𝑎 raised to the power 𝑛 is equal to 𝑛
instances of 𝑎 multiplied together. In our case, our first base is seven, which has an exponent of two. This means we have two instances of seven in our multiplication. And since the power is two, we would normally call this a square, so it’s seven
squared. And we know that seven squared or seven times seven equals 49. So this is our first term.
The power or index in our second term is three, which we call a cube. And we have two to the power three, or two cubed. This means we have three instances of two in the multiplication, which evaluates to
eight.
Now remembering our next operation is to multiply by four and writing out what we
have so far, we have 49 plus four times eight.
And now referring back to the order of operations, we see that multiplication comes
before addition. So we evaluate four times eight first to get 32. So now we have 49 plus 32, which is 81. Hence, seven squared plus four times two cubed is equal to 81.
