12.1.1 warm - up: growth mindset\non a scale ...

### 12.1.1 Warm - Up: Growth Mindset # Brief Explanations: This is a subjective question. For example, if one believes in the power of hard - work for self - improvement, they may choose statement b. The belief in the malleability of intelligence through effort aligns with the concept of a growth mindset. # Answer: The answer depends on the individual's belief. For example, if choosing statement b: "I can get smarter if I work hard." Explanation: I believe that with dedication and effort, one can acquire new knowledge and skills, thus increasing their intelligence. ### 12.1.2 Refresher: Multiplying with Exponents # Explanation: ## Step1: Recall identity exponent law and product of powers law The identity exponent law is \(a=a^{1}\), and the product of powers law is \(a^{m}\cdot a^{n}=a^{m + n}\) ## Step2: For \(d\cdot d\) Using identity exponent law: \(d^{1}\cdot d^{1}\). Using product of powers law: \(d^{1 + 1}=d^{2}\) ## Step3: For \((4x)(x)\) First, rewrite using identity exponent law: \((4x^{1})(x^{1})\). Then, using product of powers law: \(4x^{1+1}=4x^{2}\) ## Step4: For \((- 3f)(0.5f)\) Rewrite using identity exponent law: \((-3f^{1})(0.5f^{1})\). Then, using product of powers law: \((-3\times0.5)f^{1 + 1}=-1.5f^{2}\) ## Step5: For \(5c\cdot b\cdot2c\) Rewrite using identity exponent law: \((5c^{1})\cdot(b^{1})\cdot(2c^{1})\). Rearrange and use product of powers law: \((5\times2)b^{1}c^{1 + 1}=10bc^{2}\) ## Step6: Fill the box Any variable \(a\), multiplied by itself can be rewritten as \(a\cdot a=a^{2}\) # Answer: |Expression|Equivalent Expression Using Identity Exponent Law|Equivalent Expression Using Product of Powers Law| |----|----|----| | \(d\cdot d\) | \(d^{1}\cdot d^{1}\) | \(d^{2}\) | | \((4x)(x)\) | \((4x^{1})(x^{1})\) | \(4x^{2}\) | | \((-3f)(0.5f)\) | \((-3f^{1})(0.5f^{1})\) | \(-1.5f^{2}\) | | \(5c\cdot b\cdot2c\) | \((5c^{1})\cdot(b^{1})\cdot(2c^{1})\) | \(10bc^{2}\) | For the box: \(a^{2}\)